- #1

Earthland

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- 0

## Homework Statement

Need to prove that:

,b means partial differentation with respect to b, G is the metric tensor and Γ is Christoffel symbol.

I think I could proceed with this quite well if I could understand the hint given, that I should lower the index j.

## Homework Equations

a

_{m}=G

_{mj}a

^{j}

## The Attempt at a Solution

For the first member on the left I could write

G

_{mj}G

^{jk}∂

_{k}=δ

^{k}

_{m}∂

_{k}=∂

_{k}

and else than that it should stay the same

For members on the right, lowering j would give me

v

^{α}(v

_{j,α}+Γ

_{jαβ}v

^{β})

However, what should I do with the second member on the left? And I am told that this one is the important one.